Interferometers have been known and used for a long time. Interferometry is a widely used method for measuring surface profiles (often to nano-meter resolutions) and other physical properties of materials, gases and liquids. There are many types of interferometers, characterized by their optical designs and layouts. Some classical types are Twyman-Green, Fizeau, Michaelson, Mach-Zender, and Fabry-Perot. Each of these interferometer types produces interference patterns, called interferograms. These interferograms can be used to analyze characteristics of an object under test.
Interferograms are generated by the interference of a test wavefront and a reference wavefront. The test and reference wavefronts typically originate from a common “source” wavefront; they are obtained by splitting the source wavefront. The test wavefront then obtains its “test” information by interacting with the object under test (typically by reflecting off of, or transmitting through a test object). Similarly, the reference wavefront obtains its “reference” information by interacting with a “known” reference object, such as a super polished flat glass plate. Superimposing or interfering these two wavefronts spatially (i.e. on a flat screen, or on an image sensor such as a CCD) produces an interferogram.
Interferometers require coherent superposition of a “test beam” (of light) with a “reference beam” resulting in the formation of an interferogram in the overlapping region of the two beams. This interferogram data can then be captured using various types of detectors, such as a camera, for analysis.
The spatial distribution of intensity levels within the interference pattern relates to differences in the phase of the test and reference wavefronts. Note that the reference wavefront is acted on by a known “measurement standard,” such as an optical “reference” surface, and the test wavefront is acted on by the unknown object under test. Measuring the difference between the two wavefronts allows the test wavefront to be determined. In other words, the process is akin to comparing the “unknown” test wavefront to a “known” standard, the reference wavefront.
In known phase-shifting interferometry techniques, interference between the light beams reflected from the test and reference surfaces are sampled as a function of phase shift and subsequently analyzed with a phase-shifting interferometry algorithm to extract the test surface phase map, which may be converted into physical units using the known wavelength of the laser beam.
As described above, interferometric measurements of optical surfaces are typically performed through comparison with a proper reference surface. In practice, high quality references exist only for flat and spherical surfaces. As a result, measurements of aspheric surfaces are hindered by a lack of suitable reference elements. Furthermore, the aspheric surfaces form an infinite set. That is, there are an infinite number of potential variations of aspheric surfaces, and thus it is very unlikely that a proper set of reference elements could be created to cover all types of aspheric surfaces. Two techniques are commonly used to provide such references: so called Null Lenses (NL) and Computer Generated Holograms (CGH).
The following discussion of null lenses derives from U.S. Pat. No. 6,456,382 to Ichihara et al., which describes the conventional interferometer systems using null lenses. Null lenses typically use spherical lenses comprising spherical surfaces, and zone plates wherein annular diffraction gratings are formed on plane plates. In a conventional interferometer system using a null lens, the component of the plane wave transmitted through the Fizeau surface is converted into a measurement wavefront (null wavefront) by the null element and assumes a desired aspheric design shape at a measurement reference position, following which it arrives at a test surface of a test object previously set at the reference position. The light arriving at the test surface is then reflected and interferes with the light component reflected from the Fizeau surface, and forms monochromatic interference fringes inside the interferometer system. These interference fringes are detected by a detector such as a CCD. Similar measurements can be performed using a Twyman-Green interferometer.
To accurately measure the test surface, the null element must be manufactured with advanced technology, since there must be no error in the null wavefront. Thus, the optical characteristics of the null element must be accurately measured beforehand with great precision. Based on these measurements, the shape of null wavefront is then determined by ray tracing. The manufacture of a usable null element takes a long time, which lengthens the measuring process, and adds expense to the measurement technique.
U.S. Pat. No. 5,737,079 to Burge et al. describes a method of testing aspheric surfaces by using a computer-generated hologram (CGH) that is written on the reference surface of the test plate using lithographic techniques.
However such references are expensive to make and are appropriate for testing only a specific type of aspheric surfaces for which they have been designed. Additionally, such reference elements require precision alignment of multiple optical components making the measurements rather tedious and difficult. As such, these types of references are used primarily to measure expensive optical components like mirrors and lenses for astronomical telescopes or parts of military equipment.
Other methods of aspheric measurements are based on the use of mechanical styluses that are dragged across the surface. For example, U.S. Pat. No. 4,776,101 to Ishibai describes such a measurement technique.
There are further problems with the prior art aspherical object measurement techniques. For example, in an interferometer using a standard spherical or flat reference element for measurements of aspheric surfaces, both interfering beams (test and reference) may significantly differ from each other making nulling of the interference fringes impossible. Also, both beams travel along different optical paths inside the interferometer and errors introduced by aberrations of the optical system of the interferometer cannot be compensated.
Measurements performed with these prior art types of aspheric surface interferometers generally consist of the following steps:                Placement and alignment of the measured aspheric element at the measurement location. The alignment of the measured surface is difficult and critical as the optical axis of the interferometer should be co-linear with the optical axis of the aspheric surface. Otherwise errors will be introduced to the measurements.        Recording of a series of phase shifted interferograms in order to compute a phase map.        Unwrapping the phase map to account for discontinuities in the phase map. The unwrapping of very dense fringe patterns is critical and can be quite challenging as the fringe densities can be higher then the spacing between neighboring pixels.        Ray tracing through the optical system of the interferometer based on the unwrapped phase map. The ray tracing operation removes errors due to unequal optical paths of the test and reference beams        Subtraction of the optical prescription of the aspheric surface.        
The above described procedure presents several critical problems. The alignment of the measured object with respect to the optical axis of the interferometer is done in the presence of very dense interference fringes that are usually a poor guidance for the alignment. The fringes cannot be nulled and as a result the alignment has to be done by means of mechanical features. Errors in alignment will lead to measurement errors—typically with added coma and astigmatism in the final results.
Also, unwrapping of the very dense fringes poses a significant problem as the unwrapping algorithms must take into account phase discontinuities that may exist at intervals larger than 2π. The unwrapping errors in this case can be large and can propagate quickly, rendering the resulting phase maps useless. In addition, any undesirable features in the interferograms, such as fringes resulting from surface scratches, hot spots, stray light reflections or surface blemishes, will significantly exaggerate problems with phase unwrapping.
Moreover, the ray tracing procedure based on the unwrapped phase maps obtained at the detector plane is sensitive to measurement noise. The noise typically will be amplified in the process and usually will manifest itself as spikes in the final measurement. These spikes can be of significant amplitude and although localized they have to be filtered out from the final results.
These problems will be greatly aggravated in case of measurements of off-axis aspheric surfaces, surfaces with a hole in the middle or surfaces without axial symmetry.
Thus, a method that would be capable of simplifying the alignment of the aspherical object to be measured, avoiding the unwrapping of very dense fringe patterns, and eliminating the need for ray tracing would be very desirable to overcome some of the most limiting characteristics of the prior art instruments.